Farmer Jill has a problem. She lives on a triangular plot of land that is surrounded on all three sides by a fence. Yesterday, one side of the fence was blown down in a storm. She wants to determine the length of the side that needs to be rebuilt so she can purchase enough lumber. She wants to order the lumber online and have it delivered quickly but the weather is still too poor for her to go outside and measure the length of fence. So she decides to use the lengths of the two sides that are still standing ($116$ feet and $224$ feet) and the angle between them ($58^\circ$).

1. Draw a diagram of this situation. Label all of the sides and angles for which Farmer Jill has measurements.

   Answer (a):

   

2. What is the length of the fence that needs to be replaced? Show all work. Which tool did you use?

   Hint (b):

   Use the Law of Cosines to determine the length of the missing side.

   Step (b):

   Let $c =$ the unknown side length in the diagram from part (a).

   $c^2=116^2+224^2-2(116)(224)\cos(58^\circ)$

3. What is the area of her triangular plot of land?